In arrangement shown in figure, plane wavefront of monochromatic light of wavelength `lamda` is incident on identical slits `S_(1)` and `S_(2)`. There is another pair of indentical slits `S_(3)` and `S_(4)` which are having separation `Z = (lamda D)/(2d)` Point O is on the screen at the common perpendicular bisector of `S_(1)S_(2)` and `S_(3) S_(4).I_(1)` is the intensity at point O Now the board having slits `S_(3)S_(4)` is moved upward parallel to itself and perpendicular to line AO till slit `S_(4)` is on line AO and it is observed that now intensity at point O is `I_(2)` then `(I_(2))/(I_(1))` is :

Options

A. `(1)/(2)`
B. 2
C. 1
D. 0

Answer

A

Explanation

At `S_(3)` & `S_(4)`
`Delta X =(lamda)/(4) , Delta phi =(pi)/(2)`
` I_(S_(3))=I_(0)+I_(0)=I_(S_(4)),I_(1)=4(2I_(0))=8I_(0)`
In final situation
`I_(S_(3))=0" "I_(S_(4))=4I_(0)`
`I_(2)=4I_(0)`
`:. (I_(2))/(I_(1))=(1)/(2)`.